It’s a basic rule of Spanish phonotactics. In a nutshell, the structure of a Spanish syllable does not allow it:
(C1 (C2)) (S1) V (S2) (C3 (C4))
A Spanish syllable consists of an optional onset, consisting of one or two consonants; a required nucleus, consisting of a vowel optionally preceded by and/or followed by a semivowel; and an optional coda, consisting of one or two consonants.
Now take “spa” (as in Spanish) as an example syllable. First in the onset can be any consonant (here [s]), but a second consonant is allowed only if the first is [p], [t], [k], [b], [d], [ɡ], or [f]. Furthermore, the second consonant can only be [l] or [r]. “Spa” satisfies neither of these rules, therefore it cannot occur as a syllable in a (native) Spanish word.
It just happens that the most common words which do begin with [sp-] in English begin with [esp-] in Spanish, because that was usually the original spelling. English got a lot of these words via Old French; the initial [e] was reduced to [ə] and typically dropped thereafter.
Obviously Spanish speakers have the physical ability to pronounce words beginning with [sp] and other such consonant clusters. But when learning (or borrowing words from) another language, our pronunciation is often coloured by our native tongue, hence “Esprite”.
The reason Spanish lost syllable-initial /sp/ from Latin is that this sequence of sounds is a violation of the sonority sequencing principle. Normally, sounds in a syllable are more sonorous (vowels, glides, and liquids) toward the centre of the syllable, and less sonorous (nasals, stops, and clicks) toward the beginning and end. Most languages follow this structure fairly closely, typically with a few exceptional words, most often involving clusters of /s/ + stop consonant. Latin allowed /sp/ as an exception to the SSP (and Western Romance languages like Italian still do), but Spanish does not, so /sp-/ words were altered to place the /s/ at the end of a syllable, giving /esp-/.
In other words, /sp-/ is an unusual phonetic feature, and such features are often lost during contact with other languages—in this case, contact between Vulgar Latin and the local Iberian languages.
esp: "especially", "espionage", "espresso", "espouse", etc. Some are on loan from French or Italian, but there's no rule against that spelling. (There are hardly any rules of English spelling, but that's a topic for another site. ;-)